How do you get the categories to display on single post pages?

There is a checkbox in the widget options as of version 3.2 that will display the same structure for the categories the post is in.

How do you edit the output or built in css?

Create a folder in your child theme named "advanced-sidebar-menu" copy any of the files from the "views" folder into
the folder you just created. You may edit the files at will to change the output or css?
You must have the option checked to use the built in CSS (in the widget) to be able to edit the css file in this way.
The Others will work always.

Does this support multiple instances?

Yes.

Does the menu change for each page you are on?

Yes. Based on whatever parents and children pages you are on, the menu will change automatically.

How does this work with styling the page?

As of version 1.1 this will automatically generate class names for each level for menu system.
You can add classes to your theme's style.css file to style it accordingly.
You may want to use something like margins to set the levels apart.

Screenshot of the Page widget and options

Screenshot of the Categories widget and options

3.3.0

Added the ability to have a widget title

Redesigned the entire structure to prepare for future changes

3.2.5

Bugfixes

3.2.3

Fix a bug that caused multiple category list to display of more than one category the single post was in shared the same parent

3.2.1

Fix a possible bug that may display a * Notice * error if there is nothing to display and the error reporting is set to strict when using the categories widget.

3.2.0

Added ability to have categories show on single post pages

Improved the code structure

3.0.2

*Bugfixes

3.0

Added a categories menu widget with the same functionality as the pages widget

Added the ability to edit "views" files through your child theme to edit output and css

Cleanedup the output

2.1

Added default syling.

2.0

Brought back the ability to exclude pages with support for excluding single pages from the menu.

Added the ability to display all levels of child pages always.

Added the option to select how many levels of pages to display when the "Always Display Child Pages" is selected